本文將探討雙層懸臂樑在周圍環境溫度上升時的層間應力分佈情形，由於上下兩層材料性質不一，受熱變形的程度也不一樣，層與層之間將會產生層間應力來傳遞各層之間的應力差。藉由不同溫度變化與更換材料厚度來觀察溫差大小與厚度對於層間應力的影響，以及經過多次循環負載之後的疲勞壽命預測，利用有限元素套裝軟體『ANSYS』進行模擬與分析。

模擬結果顯示，層間應力主要集中在自由端附近，應力大小會隨著溫差越大而增加，且分布範圍會因為兩層的厚度減少而縮小，但若只減少其中一層的厚度，分佈範圍縮小的程度比兩層厚度都減少來的低，可見應力分佈範圍與兩層的厚度皆相關。而將兩層的厚度都減少並不會影響層間應力的值，但若改變上下兩層厚度的比例應力值則會有所增減。本模擬使用鋁合金6061-T6與單晶矽，在厚度均相同的條件之下，欲使疲勞壽命達〖10〗^5週次以上則溫差需小於93.4度，〖10〗^6週次以上溫差需小於74.9度。

This thesis aims to discuss the interlaminar stress distribution of a bi-layer cantilever beam caused by ambient temperature change. The effects of temperature change and thickness of layers on the fatigue life of the structure are also studied. The simulation and analysis of this study have been conducted by using ANSYS.
The results show that interlaminar stresses are mainly concentrated at the free edge. The interlaminar stresses increase as the temperature increases, and the size of the stress concentration region decreases as the reduction of the thickness of both layers. However, if only the thickness of one layer changes, the size only changes slightly. The simultaneous change of the thickness of both layers will not affect the magnitude of interlaminar stresses, but the thickness change of one layer only will do so. The material properties of the layers used in this study are aluminum alloy 6061-T6 and single-crystal silicon. It is concluded that if the thickness of both layers are the same, for the fatigue life of more than 〖10〗^5 cycles, temperature change must be less than 93.4℃ ; for the fatigue life of more than 〖10〗^6 cycles, temperature change must be less than 74.9℃ .

[1] A. J. Vizzini, “Prevention of Free Delamination via Edge Alternation”, Structural Dynamics and Materials Conference, Maryland University, College Park, pp. 365-375, 1988.
[2] J. M. Whitney, C. E. Browning, W. Hoogsteden, “A Double Cantilever Beam Test for Characterizing Mode I Delamination of Composite Materials”, Journal of Reinforced Plastics and Composites, Vol.1, pp. 294-313, 1982.
[3] B. D. Davidson, “An Analytical Investigation of Delamination Front Curvature in Double Cantilever Beam Specimens”, Journal of Composite Materials, Vol.24, pp. 1124-1137, 1990.
[4] F. E. Penado, “A Closed Form Solution for the Energy Release Rate of the Double Cantilever Beam Specimen with an Adhesive Layer”, Journal of Composite Materials, Vol.27, pp. 383-407, 1993.
[5] J. A. Nairn, “Energy release rate analysis for adhesive and laminate
double cantilever beam specimens emphasizing the effect of residual stresses”, International journal of adhesion and adhesives, Vol.20, pp. 59-70, 2000.
[6] M. Meo, E. Thieulot, “Delamination modelling in a double cantilever beam”, Fifth International Conference on Composite Science and Technology, Sharjah, United Arab Emirates, 2005.
[7] 周棟爕, “邊界條件對雙層結構微懸臂樑變形之影響”, 逢甲大學材料與製造工程所碩士論文, 2008.
[8] Ealias1, Lalmoni, Mattam, “Study of Inter-laminar Shear Stress of Composite Structures”, International Journal of Emerging Technology and Advanced Engineering, Vol,3, pp. 543-552, 2008.
[9] B. A. Boley, J. H. Weiner, “Theory of Thermal Stresses”, John Wiley & Sons, New York, 1960。
[10] R. G. Budynas, J. K. Nisbett, “Shigley’s Mechanical Engineering Design”, McGraw-Hill, New York, 2011.
[11] R. C. Hibbeler, “Mechanics of Materials”, 培生教育出版集團出版， 2010。
[12]羅祖道,王震鳴, “複合材料力學進展”北京大學出版社出
版,1992.
[13] B. R. Pipes,N. J. Pagano “Interlaminar Stresses In Composite Laminates Under Uniform Axial Extension”, Journal of Composite Material, Vol.4, pp. 538-548, 1970.
[14]劉晉奇, 褚晴暉, “有限元素分析與ANSYS的工程應用”,滄海
書局,台中,2006.
[15] R. D. Cook, D. S. Malkus, M. E. Plesha, R. J. Witt, “Concepts and Applications of Finite Element Analysis”, John Wiley & Sons , New York, 2002.
[16]王勖成, “有限單元法” , 北京清華大學出版社出版, 2003.
[17]http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA606 1t6 (引用時間:2016/1/14)
[18] http://www.ioffe.ru/SVA/NSM/Semicond/Si/ (引用時間:2016/1/14)